[tex]A = (-4, 3) \ \ \ \ \rightarrow \ \ x_{A} = -4, \ \ y_{A} = 3\\B = (-2, -4) \ \ \rightarrow \ \ x_{B} = -2, \ \ y_{B} = -4\\\\\\|AB| = \sqrt{{(x_{B}-x_A})^{2}+(y_{B}-y_{A})^{2}}}\\\\\\|AB| = \sqrt{(-2-(-4))^{2}+(-4-3)^{2}} =\sqrt{(-2+4)^{2}+(-7)^{2}}} =\sqrt{2^{2}+(-7)^{2}}}=\\\\=\sqrt{49+4} = \sqrt{53}\\\\|AB| = \boxed{\sqrt{53}}[/tex]
